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RS Aggarwal Solutions Class 8 Maths Chapter 3 Squares And Square Roots
RS Aggarwal Solutions Class 8 Maths Chapter 3 Squares And Square Roots – Overview
 Definitions
The value generated by multiplying the number by itself is called the Square of a number.
The value that, when multiplied by itself, gives the original value, is the square root of a number.
For example:
(6)² = 36
Square of 6 is 36 whereas 6 is the square root of 36. Therefore, the concept of the square and square root are opposite.
 Properties Of A Square Number
 Square of any number gives a positive number.
 Square of 1 is 1.
 Square of 0 is 0.
 The Square of a number under the root gives the same number as the number under the root.
 For example (√3)² = 3
There are 2 ways to find the square root of a number correctly:
 Prime Factorisation Method
 Using Long Division Method

Squares and Square Roots of Numbers From 1 to 50
Number 
Square of Number 
Square Root of Number 
1 
1 
1.000 
2 
4 
1.414 
3 
9 
1.732 
4 
16 
2.000 
5 
25 
2.236 
6 
36 
2.449 
7 
49 
2.646 
8 
64 
2.828 
9 
81 
3.000 
10 
100 
3.162 
11 
121 
3.317 
12 
144 
3.464 
13 
169 
3.606 
14 
196 
3.742 
15 
225 
3.873 
16 
256 
4.000 
17 
289 
4.123 
18 
324 
4.243 
19 
361 
4.359 
20 
400 
4.472 
21 
441 
4.583 
22 
484 
4.690 
23 
529 
4.796 
24 
576 
4.899 
25 
625 
5.000 
26 
676 
5.099 
27 
729 
5.196 
28 
784 
5.292 
29 
841 
5.385 
30 
900 
5.477 
31 
961 
5.568 
32 
1,024 
5.657 
33 
1,089 
5.745 
34 
1,156 
5.831 
35 
1,225 
5.916 
36 
1,296 
6.000 
37 
1,369 
6.083 
38 
1,444 
6.164 
39 
1,521 
6.245 
40 
1,600 
6.325 
41 
1,681 
6.403 
42 
1,764 
6.481 
43 
1,849 
6.557 
44 
1,936 
6.633 
45 
2,025 
6.708 
46 
2,116 
6.782 
47 
2,209 
6.856 
48 
2,304 
6.928 
49 
2,401 
7.000 
50 
2,500 
7.071 
 Perfect and Imperfect Square
 Perfect Square: If a whole number is multiplied by itself to generate a given number, it is said to be a Perfect square.
Example:
25−−√=5×5−−−−√=5  Imperfect square: If a whole number is not multiplied to generate a given number, it is an imperfect square.
Example:
13−−√=3.606
 In between Squares
Suppose the 2 consecutive squares are n² and (n+1)², then the number between them is 2n.
For example:
Find the numbers between 2² and 3².
2² = 4
3² = 9
And, n = 2
Therefore, the total numbers between 4 and 9 = 2n = 4
Therefore, the numbers are 5, 6, 7, 8.
 Pythagorean Triplet
3 positive integers a, b, c which satisfies this Pythagoras theorem a²+b²=c² is called the Pythagorean Triplet and the positive integers are called Pythagorean triples.
Example: (3, 4, 5)
By evaluating we get:
32 + 42 = 52
9 + 16 = 25
Hence, 3, 4, and 5 are the Pythagorean triples.
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